Are contracts signed using electronic signatures such as NemID legally binding?

Yes, it is just as legally binding and a lot more secure to sign contracts using electronic signatures. Obviously it's also faster.

In reality, you rarely get a contract on paper anymore. Just like parties and lawyers negotiate remotely using phones and emails, contracts are being printed, signed using a pen, scanned and emailed and then a lawyer is merging the different scans at the end of a pdf containing the contract. This silly practise has lasted for many years although it is wrong on so many levels. 

The EIDAS regulation establishes a framework for electronic signatures throughout Europe.

Enforcement of digital signatures

On 8 January 2019, the Danish Supreme Court ruled in a case regarding abuse of the dignital signature NemID. Two persons had handed over usernames and passwords for their NemID to third parties, who then abused the NemID to digitally sign loan agreements in a bank.

The Supreme Court ruled that a lower court could enforce the digitally signed debt instruments against the real owners of the digital signatures although they had not signed the debt instruments themselves.

Yu can read more here (Danish).